Higher-order corrections on the denaturation of homogeneous DNA thermodynamics

Abstract

DNA denaturation, the process of separating double-stranded DNA into single strands, plays a critical role in fundamental biological processes such as transcription, replication, and repair. Despite extensive studies on its thermodynamic properties, the effects of thermal fluctuations on DNA denaturation have not yet been explored. This paper addresses this gap by developing a statistical mechanical model to analyze homogeneous DNA denaturation thermodynamics with thermal fluctuations. Using the partition function framework, this study introduces two major corrections to the entropy of the system induced by thermal fluctuations: (1) a logarithmic correction of the leading order and (2) a higher-order correction term proportional to the inverse of the entropy. Analytical calculations and numerical analysis reveal that these corrections significantly influence the thermodynamic properties, including specific heat and free energy, leading to a more nuanced understanding of the DNA melting process. The corrected entropy modifies the specific heat profile, resulting in a sharp peak that reflects a first-order phase transition during DNA denaturation. The inclusion of higher-order corrections introduces asymmetry in the specific heat curve, highlighting the cooperative behavior of DNA melting. Furthermore, the free-energy analysis suggests the presence of intermediate states during strand separation, which are critical for understanding the initiation and propagation of the denaturation process. The results align well with experimental DNA melting profiles, particularly in the transition region, and provide insights into the microscopic mechanisms underlying DNA melting. This study not only advances the theoretical framework for DNA denaturation by explicitly incorporating thermal fluctuations but also offers a platform for future experimental validation and applications in biological systems. These findings have broader implications for understanding DNA stability under physiological conditions, cellular processes such as transcription initiation, and the role of ionic environments in modulating DNA thermodynamics.